What do the following two equations represent? $x+3y = -4$ $-4x-12y = -2$
Answer: Putting the first equation in $y = mx + b$ form gives: $x+3y = -4$ $3y = -x-4$ $y = -\dfrac{1}{3}x - \dfrac{4}{3}$ Putting the second equation in $y = mx + b$ form gives: $-4x-12y = -2$ $-12y = 4x-2$ $y = -\dfrac{1}{3}x + \dfrac{1}{6}$ The slopes are equal, and the y-intercepts are different, so the lines are parallel.